Problem: Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}-7x+9y &= -2 \\ -x+3y &= -6\end{align*}$
Explanation: Begin by moving the $y$ -term in the second equation to the right side of the equation. $-x = -3y-6$ Divide both sides by $-1$ to isolate $x$ $x = {3y + 6}$ Substitute this expression for $x$ in the first equation. $-7({3y + 6}) + 9y = -2$ $-21y - 42 + 9y = -2$ Simplify by combining terms, then solve for $y$ $-12y - 42 = -2$ $-12y = 40$ $y = -\dfrac{10}{3}$ Substitute $-\dfrac{10}{3}$ for $y$ in the top equation. $-7x+9( -\dfrac{10}{3}) = -2$ $-7x-30 = -2$ $-7x = 28$ $x = -4$ The solution is $\enspace x = -4, \enspace y = -\dfrac{10}{3}$.